MathDB

5

Part of 2022 Czech-Polish-Slovak Junior Match

Problems(2)

integer divisible by n + 1, n + 2, ..., n + 9 also by n+10

Source: 2022 Czech-Polish-Slovak Match Junior, individual p5 CPSJ

9/3/2022
An integer n≥1n\ge1 is good if the following property is satisfied: If a positive integer is divisible by each of the nine numbers n+1,n+2,...,n+9n + 1, n + 2, ..., n + 9, this is also divisible by n+10n + 10. How many good integers are n≥1n\ge 1?
number theorydivisible
computational geo with regular nonagon

Source: 2022 Czech-Polish-Slovak Match Junior, team p5 CPSJ

9/3/2022
Given a regular nonagon A1A2A3A4A5A6A7A8A9A_1A_2A_3A_4A_5A_6A_7A_8A_9 with side length 11. Diagonals A3A7A_3A_7 and A4A8A_4A_8 intersect at point PP. Find the length of segment PA1P A_1.
geometrynonagon